Quadratic Applications Retest

Front

What is the general form of a quadratic function?

Back

The general form of a quadratic function is f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What does the variable 't' represent in the context of height equations for objects in motion?

Back

In the context of height equations for objects in motion, 't' represents time in seconds.

Front

How do you determine the time it takes for an object to hit the ground using a height equation?

Back

To determine the time it takes for an object to hit the ground, set the height equation equal to zero and solve for 't'.

Front

What is the significance of the coefficient 'a' in a quadratic function?

Back

The coefficient 'a' determines the direction of the parabola: if 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

Front

How can you find the maximum height of a projectile modeled by a quadratic function?

Back

The maximum height of a projectile can be found using the vertex formula t = -b/(2a), where 'b' and 'a' are coefficients from the quadratic equation.

Front

What is the vertex of a parabola, and why is it important in projectile motion?

Back

The vertex of a parabola is the highest or lowest point of the graph, representing the maximum or minimum height of the projectile in motion.

Front

In the equation h(t) = -16t² + 256, what does the term '256' represent?

Back

In the equation h(t) = -16t² + 256, the term '256' represents the initial height from which the object is dropped.

Front

What is the formula to calculate the height of an object at a given time using a quadratic equation?

Back

The height of an object at a given time can be calculated using the quadratic equation h(t) = at² + bt + c, where 'a', 'b', and 'c' are constants.

Front

How do you find the horizontal distance traveled by a projectile modeled by a quadratic equation?

Back

To find the horizontal distance traveled, you can evaluate the quadratic equation at the time when the height is zero.

Front

What is the role of gravity in the height equations of projectiles?

Back

Gravity is represented by the negative coefficient of the t² term in the height equations, typically -16 in feet per second squared.